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CSC 231 Discrete Structures and Its Applications. (DISCRETE MATHEMATICS) (ONLY ANSWER IF YOU KNOW DISCRETE STRUCTURES....

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CSC 231 Discrete Structures and Its Applications. (DISCRETEMATHEMATICS) (ONLY ANSWER IF YOU KNOW DISCRETE STRUCTURES. PLEASEDON'T GUESS) (This is GENERALIZED PERMUTATIONS ANDCOMBINATIONS)

TO ANSWER THE QUESTION YOU HAVE TO FIRST FIGURE OUT IF IT'S'r-permutations with repetition' or 'r-combinations withrepetition'

1, How many PIN numbers of length 4 have at least one digit '9'?(hint: first find how many have a first digit '9', how many have asecond digit '9',… then add it up.)


2. How many PIN numbers of length 4 have exactly one digit '9'?(hint: if the first digit is '9', how many choices remain for thesecond, third and fourth digit? Then think about if the seconddigit is ‘9’).


3. How many PIN numbers of length 4 either Start and End with '0'or have at least one digit '9'?

4.Show that if there are 30 students in a class, then at leasttwo have last names that begin with the same letter. What is thename of the principle you can apply?

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I HAVE EXPLAINED EACH OF THE 4 SOLUTION TO THE ABOVE MENTIONED 4PROBLEMS BY WRITING ON A PAPERPLEASE READ IT CAREFULLY    See Answer
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